Recently, there has been tremendous interest in industry 4.0 infrastructure to address labor shortages in global supply chains. Deploying artificial intelligence-enabled robotic bin picking systems in real world has become particularly important for reducing stress and physical demands of workers while increasing speed and efficiency of warehouses. To this end, artificial intelligence-enabled robotic bin picking systems may be used to automate order picking, but with the risk of causing expensive damage during an abnormal event such as sensor failure. As such, reliability becomes a critical factor for translating artificial intelligence research to real world applications and products. In this paper, we propose a reliable object detection and segmentation system with MultiModal Redundancy (MMRNet) for tackling object detection and segmentation for robotic bin picking using data from different modalities. This is the first system that introduces the concept of multimodal redundancy to address sensor failure issues during deployment. In particular, we realize the multimodal redundancy framework with a gate fusion module and dynamic ensemble learning. Finally, we present a new label-free multi-modal consistency (MC) score that utilizes the output from all modalities to measure the overall system output reliability and uncertainty. Through experiments, we demonstrate that in an event of missing modality, our system provides a much more reliable performance compared to baseline models. We also demonstrate that our MC score is a more reliability indicator for outputs during inference time compared to the model generated confidence scores that are often over-confident.